How to find the volume of a cylinder
How to find the volume of a cylinder: square the radius, multiply by π, then multiply by the height: V = πr²h. The radius is half the diameter, and both measurements must use the same unit. The answer comes out in cubic units, such as cubic inches, cubic feet or cubic centimeters.
Contents
- The formula for the volume of a cylinder
- How to calculate the volume of a cylinder, step by step
- Worked examples in inches, feet, centimeters and meters
- Volume of a cylinder: quick reference
- How to determine the volume of a cylinder from other measurements
- Special cylinders: when the basic formula needs a tweak
- Common mistakes when finding the volume of a cylinder
- How the dimensions change the volume
- Practice and check your answers
- FAQ
V = π × r² × h. With r = 3 ft and h = 5 ft: π × 9 × 5 = 141.37 ft³ (about 1,057.5 US gallons).
The calculator above does the arithmetic and shows each step, so you can compare it with your own working. The rest of this guide explains the method by hand, with worked examples in inches, feet, centimeters and meters, then the cases where the plain formula needs an adjustment.
The formula for the volume of a cylinder
A cylinder has two identical circular bases joined by a curved side. Every slice cut parallel to the base is the same circle, so the volume is the area of that circle multiplied by the height:
V = π × r² × h
- r is the radius of the base, the distance from the center of the circle to its edge.
- h is the height, measured square to the base. For a cylinder lying on its side, it is the length.
- π (pi) is about 3.14159. Use the π key of your calculator for the most accurate result.
The part π × r² is the area of the circular base. That is why the method is often summed up as "base area times height", the same rule used for any prism. If you want to see where the formula comes from, the page on the derivation of the cylinder volume formula builds it from stacked disks and from an integral.
How to calculate the volume of a cylinder, step by step
- Measure the radiusIf you measured straight across the circle, you have the diameter: divide it by 2. A can 3 in wide has a radius of 1.5 in.
- Measure the heightMeasure from one base to the other, at right angles to the base. For capacity, use inside measurements.
- Put both in the same unitConvert inches to feet, centimeters to meters, or the other way around, before you multiply.
- Square the radiusMultiply the radius by itself: 1.5 × 1.5 = 2.25.
- Multiply by πThis gives the area of the base: π × 2.25 ≈ 7.0686 in².
- Multiply by the height7.0686 × 4.5 ≈ 31.81 in³. Write the unit as a cube: in³, ft³, cm³ or m³.
That is the whole method. If your diameter is the measurement you trust, the page on the volume of a cylinder with the diameter shows the version of the formula that skips the halving step, V = πd²h ÷ 4.
Worked examples in inches, feet, centimeters and meters
Every number below was computed with the full value of π and rounded only at the end.
Example 1: a small can, in inches
A can is 3 in across and 4.5 in tall. The radius is 3 ÷ 2 = 1.5 in. The base area is π × 1.5² = π × 2.25 ≈ 7.0686 in². The volume is 7.0686 × 4.5 ≈ 31.81 in³. In exact form, that is 10.125π in³. Divided by 231, it is about 0.138 US gallons; multiplied by 16.387064, it is about 521 cm³, or 521 mL.
Example 2: a water tank, in feet
A round tank has a radius of 3 ft and a height of 5 ft. The base area is π × 3² = 9π ≈ 28.274 ft². The volume is 28.274 × 5 ≈ 141.37 ft³. One cubic foot holds 7.48052 US gallons, so the tank holds about 1,057.5 gallons when full. Divided by 27, the same volume is about 5.236 cubic yards. Tanks that are only partly full are handled by the cylindrical tank volume calculator.
Example 3: a jar, in centimeters
A jar has an inside radius of 4 cm and a height of 10 cm. The base area is π × 4² = 16π ≈ 50.265 cm². The volume is 50.265 × 10 ≈ 502.65 cm³. Since 1,000 cm³ make one liter, the jar holds about 0.503 L.
Example 4: a silo section, in meters
A cylindrical bin is 2.4 m in diameter and 3 m tall. The radius is 1.2 m. The base area is π × 1.2² = π × 1.44 ≈ 4.5239 m². The volume is 4.5239 × 3 ≈ 13.572 m³, which is 13,572 L, because one cubic meter holds 1,000 liters.
Example 5: mixed units, inches and feet
A plastic drum is 18 in across and 4 ft tall. The units differ, so convert first. You can work in inches or in feet; the answer is the same.
| Step | Working in inches | Working in feet |
|---|---|---|
| Radius | 18 ÷ 2 = 9 in | 9 in = 0.75 ft |
| Height | 4 ft = 48 in | 4 ft |
| Base area | π × 81 ≈ 254.47 in² | π × 0.5625 ≈ 1.7671 ft² |
| Volume | 254.47 × 48 ≈ 12,214.5 in³ | 1.7671 × 4 ≈ 7.0686 ft³ |
| US gallons | 12,214.5 ÷ 231 ≈ 52.88 gal | 7.0686 × 7.48052 ≈ 52.88 gal |
Note that 12,214.5 ÷ 1,728 ≈ 7.0686: one cubic foot is 12 × 12 × 12 = 1,728 cubic inches, not 12.
Example 6: mixed units, centimeters and meters
A planter is 30 cm across and 1.2 m tall. In centimeters, r = 15 cm and h = 120 cm. The base area is π × 225 ≈ 706.86 cm², and the volume is 706.86 × 120 ≈ 84,823 cm³, or about 84.82 L. In meters, r = 0.15 m and h = 1.2 m give about 0.0848 m³, the same amount.
Volume of a cylinder: quick reference
| Cylinder | r | h | Volume | Capacity |
|---|---|---|---|---|
| Can | 1.5 in | 4.5 in | 31.81 in³ | 0.138 US gal |
| Tank | 3 ft | 5 ft | 141.37 ft³ | 1,057.5 US gal |
| Jar | 4 cm | 10 cm | 502.65 cm³ | 0.503 L |
| Bin | 1.2 m | 3 m | 13.572 m³ | 13,572 L |
| Drum | 9 in | 48 in | 12,214.5 in³ | 52.88 US gal |
| Planter | 15 cm | 120 cm | 84,823 cm³ | 84.82 L |
How to determine the volume of a cylinder from other measurements
You do not always have the radius and height in hand. The formula can be turned around or fed with a different measurement:
- From the circumference. Wrap a tape around the outside, then r = C ÷ 2π. This is the easiest way to measure a large tank or a tree trunk.
- Finding the radius from the volume. If you know V and h, then r = √(V ÷ πh). The guide on how to find the radius of a cylinder covers this and the versions that start from the surface area.
- Finding the height from the volume. If you know V and r, then h = V ÷ πr². The page on how to find the height of a cylinder works through tanks sized in gallons and liters.
Special cylinders: when the basic formula needs a tweak
The formula V = πr²h covers any straight, solid, round cylinder. Other shapes reuse the same idea with a small change:
- Tubes and pipes. A pipe wall is the space between two circles. The material volume is π(R² − r²)h, where R is the outer radius and r the inner one; see the hollow cylinder volume guide.
- Half and quarter cylinders. Cut a cylinder along its length and each half holds πr²h ÷ 2. Troughs and arched shapes are covered on the half cylinder volume page, along with any other sector angle.
- Slanted cylinders. A leaning cylinder keeps the same volume as a straight one with the same base and the same perpendicular height, not the slanted side. The page on the volume of an oblique cylinder explains why.
- Oval cross-sections. When the base is an ellipse with semi-axes a and b, the volume is πabh. The elliptical cylinder volume page shows how to measure an oval tank.
- Rounded ends. A cylinder capped with a half sphere holds πr²h + ⅔πr³. Capsules, silos and propane tanks are worked out on the page about a cylinder with a hemisphere.
- Comparing shapes. A cone fits one third of the matching cylinder, and a sphere two thirds of the cylinder that wraps it. The ratios are explained on the page comparing the volume of a cylinder, cone and sphere.
Common mistakes when finding the volume of a cylinder
The most frequent error is using the diameter in place of the radius. For the 3 in can, π × 3² × 4.5 gives 127.23 in³, four times the true 31.81 in³, because the radius is squared.
- Mixing units. A radius in inches and a height in feet produce a number that means nothing. Convert one of them first, as in example 5.
- Squaring the wrong term. Only the radius is squared: π × r² × h. Writing 2 × π × r × h instead gives the curved surface area, not the volume.
- Converting cubic units like straight units. One foot is 12 inches, but one cubic foot is 1,728 cubic inches. One meter is 100 cm, but one cubic meter is 1,000,000 cm³.
- Rounding too early. Rounding π to 3.14 changes the result by about 0.05 %; rounding the base area to one digit before multiplying can cost far more. Keep the full values until the last step.
- Outside instead of inside dimensions. For how much a container holds, measure inside the walls. The outside measurements include the wall itself.
- Confusing volume and area. Volume is the space inside, in cubic units. The surface area of a cylinder is the material on the outside, in square units.
How the dimensions change the volume
Because the radius is squared, it has more effect than the height. Double the height and the volume doubles. Double the radius and the volume is multiplied by four. Triple the radius and it is multiplied by nine. This explains why a slightly wider tank holds much more than a slightly taller one. For instance, the 3 ft by 5 ft tank in example 2 holds about 141.37 ft³; with a 6 ft radius and the same height, it would hold four times as much, about 565.49 ft³.
A useful check: the volume of a cylinder must be less than the volume of the box that fits around it, (2r)² × h, and more than half of it. The exact share is π ÷ 4, about 78.5 %. For the can in example 1, the box is 3 × 3 × 4.5 = 40.5 in³, and 31.81 is 78.5 % of that.
Practice and check your answers
The best way to learn how to find the volume of a cylinder is to work a few problems yourself, then check them. The cylinder volume practice problems go from simple radius-and-height questions to unit conversions, reverse problems and word problems, each with a worked answer. You can check any result with the cylinder volume calculator on the home page.
FAQ
How do you find the volume of a cylinder?
Measure the radius r and the height h in the same unit. Square the radius, multiply by π, then multiply by the height: V = πr²h. A cylinder with r = 3 ft and h = 5 ft holds π × 9 × 5 ≈ 141.37 ft³.
How do I find the volume of a cylinder with the diameter?
Halve the diameter to get the radius, then use V = πr²h. You can also use V = πd²h ÷ 4 directly. A 3 in wide, 4.5 in tall cylinder holds π × 3² × 4.5 ÷ 4 ≈ 31.81 in³.
What units is the volume of a cylinder in?
Cubic units of the length you measured: in³, ft³, cm³ or m³. Convert afterwards: in³ ÷ 231 = US gallons, ft³ × 7.48052 = US gallons, cm³ ÷ 1,000 = liters, m³ × 1,000 = liters.
How do you calculate the volume of a cylinder when the units are different?
Convert one measurement first so both are in the same unit. For a radius of 9 in and a height of 4 ft, use 9 in and 48 in (V ≈ 12,214.5 in³) or 0.75 ft and 4 ft (V ≈ 7.0686 ft³). Both are the same volume.
Should I use 3.14 or the π key?
Use the π key when you can. Rounding π to 3.14 makes the answer about 0.05 % too small: 31.79 in³ instead of 31.81 in³ for the 3 in by 4.5 in cylinder. Many textbooks accept 3.14, so follow the rounding your teacher asks for.
Related
- Volume with diameterVolume of a cylinder with the diameter: V = πd²h ÷ 4. Calculator, worked examples in inches, feet and cm, and how to find the diameter from the volume.
- Radius of a cylinderHow to find the radius of a cylinder from its volume, surface area, circumference or diameter. Formulas, calculator and worked examples in inches and cm.
- Practice problemsVolume of a cylinder worksheet: 15 graded practice problems, from basic radius and height to units, reverse and word problems, each with a worked answer.
Updated October 12, 2026